Publication: Thermodynamics of the Schwinger and Thirring models
Loading...
Official URL
Full text at PDC
Publication Date
1987-05-15
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Soc
Citations
Exportar
Abstract
The thermodynamical partition functions for both the Schwinger and Thirring models are evaluated. The imaginary time formalism of quantum field theory at finite temperature and pathintegral methods are used. For the Schwinger model, the partition function displays two features: (i) no physical (transverse) photons exist in 1+1 dimensions; (ii) the theory also describes just free massive bosons. For the Thirring model, the partition function equals that for free massless fermions. The complete thermodynamical propagators and the energies per unit volume at finite temperature are also given.
Description
© 1987 The American Physical Society.
Partial support given by Plan Movilizador de Altas Energias (Proyecto de Investigacion AE86-0029), Comision Asesora de Investigacion Cientifica y Tecnica, Spain, is acknowledged. One of us (R.F.A.-E.) is grateful to the Council for International Exchange of Scholars for support through a Fulbright/MEC Grant, and to Professor B. Zurnino for the kind hospitality extended to him at the Theoretical Physics Group, Lawrence Berkeley Laboratory
UCM subjects
Unesco subjects
Keywords
Citation
1 H. A. Weldon, Phys. Rev. D 26, 1394 (1982).
2 H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo-Field
Dynamics and Condensed States (North-Holland, Amsterdam, 1982).
3 J. F, Donoghue, B. R. Holstein, and R. W. Robinett, Phys. Rev. D 30, 2561 (1984); G. Peressutti and B. S. Skagerstam,
Phys. Lett. 110B, 406 (1982); R. Tarrach, ibid. 133B, 259 (1983).
4 L. Dolan and R. Jackiw, Phys. Rev. D 9 3320 (1974).
5 A. J. Niemi and G. W. Semenoff, Nucl. Phys. B230, 181 (1984).
6 C. Bernard, Phys. Rev. D 9, 3312 (1974)~
7 T. Matsubara, Frog. Theor. Phys. 14, 351 (1955).
8 Y. Takahashi and H. Umezawa, Collect. Phenom. 2, 55 (1975).
9 I. Ojima, in Progress in Quantum Field Theory, edited by H. Ezawa and S. Kamefuchi (North-Holland, Amsterdam, to be published).
10 The integration over A yields the l3-independent constant (see
Ref. 6) det( p ) ~p ezp 2 d x 2 (x)D ' "(&)~„(&) penod)e P which has been absorbed into the normalization constant N of Eq. (2.3). Actually, the analogue of the representation (2.3) for 1 + 3 dimensions has been obtained a long time ago by E. S. Fradkin, Dok. Akad. Nauk. SSSR 125, 66 (1959) [Sov. Phys. Dokl. 4, 327 (1959)];Nucl. Phys. 12, 465 (1959).
11 H. M. Fried, Functional Methods and Models in Quantum Field Theory (MIT Press, Cambridge, MA, 1972).
12 P. D. Morley and M. B. Kislinger, Phys. Rep. 51, 63 (1979).
13 J. Schwinger, Phys. Rev. 128, 2425 (1962)~
14 F. Ruiz Ruiz and R. F. Alvarez-Estrada, Phys. Lett. 180B, 153 (1986); 182B, 354 (1986).
15 G. G. MacFarlane, Philos. Mag. 40, 188 (1949); H. W. Braden, Phys. Rev. D 25, 1028 (1982).
16 A general zero-temperature Hamiltonian solution of the chiral Schwinger model, which, in particular, displays these facts for the ordinary (nonchiral) one is given in A. J. Niemi and G. W. Semenoff, Phys. Lett. 175B, 439 (1986). For a more general discussion of the boson-fermion relationship in two spacetime dimensions see, for instance, P. Garbaczewki, Phys. Rep. 36C, 65 (1978), and references therein